We prove that the total chromatic number of any graph with maximum degree is at most plus an absolute constant. In particular, we show that for su ciently large, the total chromat...
For an undirected graph G = (V, E), let Gn denote the graph whose vertex set is V n in which two distinct vertices (u1, u2, . . . , un) and (v1, v2, . . . , vn) are adjacent iff ...